326 R. Damania, P.G. Fredriksson J. of Economic Behavior Org. 41 2000 315–335
ually rational strategy for each firm
19
. Rearranging Eq. 17 defines a critical discount rate:
r
L
≡ π
cc i
Q
cc
, t
S
m i
,S
m j
− π
cn i
Q
cn
, t
w
π
cd i
Q
cd
, t
0,S
m j
− π
cc i
Q
cc
, t
S
m i
,S
m j
. 18
Observe that from Eq. 17 it follows that equilibrium contributions of S
m i
, i = 1, 2, i 6= j, can be sustained by this strategy if the prevailing discount rate is r ≤ r
L
. For future reference, Lemma 3 describes the manner in which each firm’s contribution
affects its rival’s incentive to free ride.
Lemma 3.
Each firm’s incentive to free ride is increasing in its rival’s contributions. Lemma 3 is the lobbying game counterpart of Lemma 1. It simply reveals that an increase
in contributions by one firm renders free riding more attractive to its rival. Lemma 4 shows the effect of the pollution tax on collusive profits.
Lemma 4. Ceteris paribus, collusive profits are decreasing in the pollution tax.
Lemma 4 shows that a lower pollution tax unambiguously increases profits, although from Proposition 1 the level of collusion decreases. Thus, the direct effect on profits of the
tax dominates the indirect effect via collusion. Having defined the conditions necessary to make lobbying feasible in an infinitely re-
peated game, we now turn to the equilibrium properties.
5. Equilibrium properties
We now explore the factors which influence the incentive to form a lobby group. We, therefore, begin by assuming that lobbying is feasible which by Eqs. 17 and 18 requires
of the prevailing discount rate that r ≤ r
L
The properties of the resulting equilibria depend not only on the level of the prevailing discount rate but also on the relative positions of the
critical levels r
q
and r
L
as defined in Eqs. 8 and 18, respectively. We distinguish three cases corresponding to Cases A1–A3 above.
Case B1: Assume r = r
q
≤ r
L
. Lobbying is incentive compatible and tacit collusion in the output stage is sustainable. Since r = r
q
the incentive compatibility constraint in Eq. 7.2 binds with equality, thus as noted in Section II output levels lie between the Cournot
and the joint profit maximizing levels. Case
B2: Assume r ≤ r
L
and r r
q
. In this case lobbying and tacit collusion in the output stage are sustainable. Since r r
q
, the incentive compatibility constraint in Eq. 7.2 holds with slack, and output is at the joint profit maximizing level.
Case B3: Assume r ≤ r
L
and r r
q
. From Eq. 17, lobbying is incentive compatible since r ≤ r
L
. However, since r r
q
, tacit collusion in the output stage of the game cannot be sustained. Thus, output levels are set at the Cournot–Nash equilibrium. In this case lobbying
takes place even in the absence of tacit collusion in the output market.
19
The incentive compatibility constraint in Eq. 17 is based on the implicit assumption that tacit collusion in the output stage is feasible, even in the absense of lobbying Eschewing this assumption would merely strengthen the
results outlined below without altering the qualitative conclusions.
R. Damania, P.G. Fredriksson J. of Economic Behavior Org. 41 2000 315–335 327
In what follows, we are interested in analyzing the manner in which changes in the degree of collusion in the output market affect the incentive to contribute to the lobby group. Hence,
we focus only on those equilibria in which lobbying is feasible and there is constrained tacit collusion.
20
This is equivalent to assuming that r = r
q
≤ r
L
, i.e., Case B1.
6. Lobby group formation
